Let a and b be the solutions to 7x^2 + x - 5 = 0. What is the solution to (a - 4)(b - 4)?
Hint:
Factor the equation, then find the roots of it (a+#)(b+#) Then, do (a-4)(b-4)
Hope this helped!
(a - 4) (b - 4) =
(ab)^2 - 4(a +b) + 16 (1)
By Vieta
The sum of the roots a + b = -1/7 (2)
And the product of the roots, ab = -5/7 = -5/7 (3)
Subbing (2) and (3) into (1) we get that
(-5/7)^2 - 4(-1/7) + 16 =
25/49 + 4/7 + 16 =
[25 + 28 + 784 ] / 49
837 / 49
+2094 
